I’m using the latest version of everything and I was wondering if it uses the cloud at all. Are there any kind of tracking or automatic diagnostic reporting?
Does it use the internet at all, other than for updates and installing plugins?

There’s the telemetry as stated on the “sonar.properties” file, but it can be disabled:

# Telemetry - Share anonymous SonarQube statistics
# By sharing anonymous SonarQube statistics, you help us understand how SonarQube is used so we can improve the product to work even better for you.
# We don't collect source code or IP addresses. And we don't share the data with anyone else.
# To see an example of the data shared: login as a global administrator, call the WS api/system/info and check the Statistics field.
#sonar.telemetry.enable=true